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We present a diffeomorphic image registration algorithm to learn spatial transformations between pairs of images to be registered using fully convolutional networks (FCNs) under a self-supervised learning setting. The network is trained to estimate diffeomorphic spatial transformations between pairs of images by maximizing an image-wise similarity metric between fixed and warped moving images, similar to conventional image registration algorithms. It is implemented in a multi-resolution image registration framework to optimize and learn spatial transformations at different image resolutions jointly and incrementally with deep self-supervision in order to better handle large deformation between images. A spatial Gaussian smoothing kernel is integrated with the FCNs to yield sufficiently smooth deformation fields to achieve diffeomorphic image registration. Particularly, spatial transformations learned at coarser resolutions are utilized to warp the moving image, which is subsequently used for learning incremental transformations at finer resolutions. This procedure proceeds recursively to the full image resolution and the accumulated transformations serve as the final transformation to warp the moving image at the finest resolution. Experimental results for registering high resolution 3D structural brain magnetic resonance (MR) images have demonstrated that image registration networks trained by our method obtain robust, diffeomorphic image registration results within seconds with improved accuracy compared with state-of-the-art image registration algorithms.

Prior work has shown that there is substantial interindividual variation in the spatial distribution of functional networks across the cerebral cortex, or functional topography. However, it remains unknown whether there are sex differences in the topography of individualized networks in youth. Here, we leveraged an advanced machine learning method (sparsity-regularized non-negative matrix factorization) to define individualized functional networks in 693 youth (ages 8 to 23 y) who underwent functional MRI as part of the Philadelphia Neurodevelopmental Cohort. Multivariate pattern analysis using support vector machines classified participant sex based on functional topography with 82.9% accuracy ( P < 0.0001). Brain regions most effective in classifying participant sex belonged to association networks, including the ventral attention, default mode, and frontoparietal networks. Mass univariate analyses using generalized additive models with penalized splines provided convergent results. Furthermore, transcriptomic data from the Allen Human Brain Atlas revealed that sex differences in multivariate patterns of functional topography were spatially correlated with the expression of genes on the X chromosome. These results highlight the role of sex as a biological variable in shaping functional topography.

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